Moisture activated latent curing adhesive or sealant

ABSTRACT

The invention relates to a novel poly(ethylene oxide)imine; a novel amine reactive moiety; a novel moisture activated latent curing adhesive or sealant mixture comprising (1) a ketimine or aldimine, and (2) an amine reactive moiety; and a novel moisture activated latent curing adhesive or sealant comprising the reaction product of (1) and (2).

FIELD OF THE INVENTION

The invention relates to a novel poly(ethylene oxide)imine; a novelamine reactive moiety; a novel moisture activated latent curing adhesiveor sealant mixture comprising (1) a ketimine or aldimine, and (2) anamine reactive moiety; and a novel moisture activated latent curingadhesive or sealant comprising the reaction product of (1) and (2).

BACKGROUND OF THE INVENTION

When surgery is performed and wound closure is completed, there is anunmet need for an adhesive or sealant material that will seal the woundsite and prevent fluid leakage in, for example, a vessel anastomosis orlung resection. Generally, the key requirements of a tissueadhesive/sealant are:

-   -   (1) In use, the adhesive/sealant must mimic the mechanical        performance of undamaged tissue;    -   (2) The adhesive/sealant should provide sufficient tack for        “primary” fixation with the opportunity for manipulation and        re-alignment prior to setting strongly;    -   (3) Any exothermic process involved in the curing of the        adhesive/sealant should not damage the surrounding tissue;    -   (4) The adhesive/sealant must not elicit any toxic response by        the surrounding healthy tissue and should facilitate the        re-growth of new tissue where possible;    -   (5) The adhesive/sealant should not liberate harmful degradation        products;    -   (6) The adhesive/sealant should degrade, and as it does so, it        should be replaced by new tissue with minimal scarring; and    -   (7) Any biodegradation products should not accumulate in the        body but should be eliminated naturally either by excretion or        incorporation into the natural biochemical cycle.        [“Polymeric Biomaterials”, 2^(nd) Ed., Marcel Dekker        Inc., (2002) pp. 716]

Latent curing adhesives are well known in the field of industrialcoatings, adhesives and sealants. For example, a latent curing adhesivemay be the reaction product of a two-component mixture, one componentbeing the reactive moiety, such as an epoxy or silicone resin, and theother component being the latent curing agent. More specifically, thelatent curing agent may be present in the two component mixture in anon-reactive form, i.e., latent form, during manufacture, storage andnon-use, but may then be converted to a reactive curing agent uponapplication and use. As an example, the latent curing agent may beconverted to a reactive curing agent in the presence of moisture that ispresent in the environment or supplied to the site upon use. It is wellknown in the art, for example, that a ketimine moiety may be used as alatent curing agent that may be converted to a reactive curing agent,i.e., an amine moiety, in the presence water. After the ketimine moietyhas been converted to its amine counterpart, the amine moiety may thenreact with the second component of the mixture, i.e., a reactive moietysuch as an epoxy or silicone resin, to form the desired adhesive and/orsealant. Examples of various ketimines and latent curing adhesives aredescribed in U.S. Pat. No. 6,525,159.

However, the latent curing adhesives described in the prior art areintended for industrial use, and are unsuitable for human use as aninternal adhesive or sealant. Therefore, it is desirable to have amoisture-activated latent curing adhesive or sealant mixture that iscapable of polymerizing in vivo to form an internal tissue adhesive orsealant. Additionally, it is desirable that such a moisture activatedlatent curing adhesive or sealant mixture be simple to use and handle,i.e., can be delivered as a single mixture, and is in the form of aflowable mixture that can be delivered to a surgical site, via forexample, a syringe.

SUMMARY OF THE INVENTION

The invention relates to a poly(ethylene oxide)imine; an amine reactivemoiety; a moisture activated latent curing adhesive or sealant mixturecomprising (1) a ketimine or aldimine and (2) an amine reactive moiety;and a moisture activated latent curing adhesive or sealant comprisingthe reaction product of (1) and (2).

BRIEF DESCRIPTION OF THE FIGURES

FIG. I illustrates a general pathway for the reaction of a ketimine andan amine reactive moiety.

FIG. II illustrates the moisture activated curing of an isocyanatemacromer with a ketimine according to Example 2.

FIG. III illustrates synthesis of an amine reactive moiety having anelectrophilic group and absorbable ester linkages.

DETAILED DESCRIPTION OF THE INVENTION

The invention relates to a poly(ethylene oxide)imine; an amine reactivemoiety having electrophilic groups; a moisture activated latent curingadhesive or sealant mixture comprising (1) a ketimine or aldimine and(2) an amine reactive moiety; and a moisture activated latent curingadhesive or sealant comprising the reaction product of (1) and (2). Thelatent curing ability of the adhesive or sealant mixture describedherein is imparted by blocking a reactive primary amine with a ketone oraldehyde to form a poly(ethylene oxide)imine. The reaction of thepoly(ethylene oxide)imine with the electrophilic groups of an aminereactive moiety is relatively slow, such that these two components maybe in intimate contact in a mixture, in the absence of moisture, forextended periods of time, i.e., for up to about 5 hours withoutpremature gelling. By comparison, when the two component mixture issubjected to moisture, the poly(ethylene oxide)imine is “de-blocked”with water to reform the primary amine within about 30 seconds to 3minutes, which then immediately reacts with the electrophilic groups ofthe amine reactive moiety.

The latent curing adhesive or sealant mixture according to the presentinvention has multiple medical applications and may be used in manytypes of surgery, including, but not limited to, cardiovascular,peripheral-vascular, cardio-thoracic, gynecological, neuro- and generalabdominal surgery.

For example, the latent curing adhesive or sealant may be used as aninternal surgical adhesive in orthopedic procedures such as anteriorcruciate ligament repair, meniscal tear repair (or as a hydrogel for thereplacement of the meniscus), posterior capsule reconstruction, rotatorcuff repair, and as a bone adhesive. It could also be used as anadhesive for lung volume reduction, patch fixation, subcutaneous tissuerepair, and aortic dissection. In particular, it can be used as stomachadhesive for stomach volume reduction, and as adhesive for mesh fixationfor hernia repair, drain fixation, valve attachment, attachment foradhesion prevention films, attachment of tissue to tissue (e.g.synthetic or biologic tissue scaffold to tissue, bioengineered tissue totissue), tissue to device (e.g. mesh, clip, film) and device to device.

Second, the latent curing adhesive or sealant mixture can be used forsubcutaneous tissue repair and for seroma prevention in procedures suchas mastectomy, breast reconstruction & augmentation, reconstructive orcosmetic abdominoplasty and liposuction, face lift, C-section,hysterectomy in obese patients, orthopedic on thigh region, incisionalhernia repair, lipoma excision, traumatic lesions, fistula treatment,graft fixation, and nerve repair.

Third, the latent curing adhesive or sealant can be used as a sealant toattach and seal dural patch products, bile duct, bile leaks in liverbed, bladder leaks, bone graft, burn graft dressing and liquid occlusivedressing. As a sealant, it can be coated on tissue, device, andtissue-device interface and it can be used as dural-cranial sealant,dural-spine sealant, cardio/peripheral vascular sealant, GI sealant(e.g. esophagus, intestine, large organ, pancreas, stomach, and gastriculcer), lung sealant, soft organ sealant (e.g. liver, spleen, pancreas),bonewax substitute, tumor sealant, staple/glue combination,sealant/hemostats combination, urethra sealant. It can be used inprocedures including, but not limited to, gastric bypass, parenchymatousorgans resection, tracheostomy, ulcerative colitis diverticulosis,radical prostatectomy, sinus reconstruction, sternotomy,choledochoduodenostomy, and gallbladder (liver) bed sealing, andcholecystectomy.

Fourth, the latent curing adhesive or sealant can be used as a filler ora periurethral bulking agent in procedures including, but not limited,to dead space removal in reconstructive and cosmetic surgeries, (e.g.plastic/cosmetic/reconstructive, face/facial defect, or void filling),urinary incontinence and other gynecologic procedures, analfissure/fistula, catheter injection into myocardium for treatingcongestive heart failure, nuclear augmentation, pancreatic/hepaticcyst/fistula obliteration, and pediatric esophogeal fistula.

Fifth, the latent curing adhesive or sealant can be used as a matrix fortissue engineering (e.g. tissue scaffolds, delivery matrix for cells,delivery matrix for brachytherapy (radiation therapy) agents, deliverymatrix for growth factors, injection matrix for in situ-forming emptycell scaffold, injection matrix for scaffold for delivery of stem cells,cell lysate, or other biologics, bioactives, pharmaceuticals, andneutraceuticals, localization matrix for chemotherapy, and localizationmatrix for contrast agent.

Sixth, the latent curing adhesive or sealant can be used as an adhesionprevention barrier in procedures such as cardiac, open chest, generalsurgery, obstetrics and gynecological surgeries, orthopedic surgeries,and spine (e.g. artificial disk).

Seventh, the latent curing adhesive or sealant can be used as anoccluding material for embolization (e.g. GI Fistula, cerebral/vascularocclusive brain aneurism, tubal occlusion, and varicose vein occlusion).

The Ketimine or Aldimine

The ketimine or aldimine may be an imine macromer such as apoly(ethylene glycol)imine represented by formula I:

where 3000≧a₁≧3; 6≧f≧2; R₁ may be a residue of a polyol, i.e.,pentaerythritol, glycerols, polyalkylene glycol, and polyols havingheteroatoms; R₁′ and R₁″ are each an alkyl group, i.e., methyl, ethyl,isopropyl or isobutyl group, alkoxy group, i.e., ethoxy or carbalkoxygroup, acetoacetate or a hydrogen; and at least one of R₁′ or R₁″ is analkyl group having from about 1 to 20 carbon atoms.

Preferably a₁ ranges from about 3 to 500; f ranges from 2 to 4; R₁ is aresidue of pentaerythritol; and R₁′ and R₁″ are each a methyl andisopropyl group. More preferably a₁ ranges from about 18 to 22, and f is4. The molecular weight of the poly(ethylene oxide)imine may range fromabout 250 to 10,000, preferably from about 250 to 4000, and morepreferably from about 250 to 1000.

An example of such a poly(ethylene oxide)imine with a pentaerythritolcore to give a 4-armed-PEG-ketimine of a molecular weight of 4,000,where a₁=18-22 is shown in Ia:

Additional examples of the poly(ethylene oxide)imine include but are notlimited to glyceraldimine and isobutylaldimine.

The Amine Reactive Moiety

The imine macromers such as the poly(ethylene oxide)imine represented byIa may be used as the latent curing agent for an amine reactive moietyhaving hydrolytically unstable ester linkages and electrophilic groups,including but not limited to isocyanate or N-hydroxy succinimide estergroups, and represented by III, IVa or IVb below:

For example, isocyanate or N-hydroxy succinimidyl terminated prepolymersare made by derivatizing the terminal hydroxyl groups of pentaerythritolethoxylate or other polyols including hydroxyl terminated linear PEGsinto carboxylate end groups by reacting them with anhydrides such as orglutaric, succinic or diglycolic anhydride, and then modifying thecarboxylate groups into isocyanate groups via Curtius rearrangement orinto the N-hydroxy succinimidyl ester groups via reaction withdisuccinimidyl carbonate. Other hydroxyl terminated polymers that may beused to carry out reactions to form isocyanate or N-hydroxy succinimidylterminated prepolymers, include without limitation, linear or multi-armpolyols derived from pentaerythritol or glycerol.

Where 3000≧a₃≧3; 6≧f₃≧2; R₃ may be a residue of a polyol, i.e.,pentaerythritol, glycerols, polyalkylene glycol, and polyols havingheteroatoms; and R₃′ may be —CH₂CH₂—, —CH₂CH₂CH₂— or —CH₂OCH₂—; and X isan electrophilic group including without limitation, isocyanate andN-hydroxysuccinimide ester.

Preferably, a₃ ranges from 3 to 500; and f₃ ranges from 2 to 4. Themolecular weight of amine reactive moiety may range from about 250 to10,000, preferably from about 250 to 4000, and more preferably fromabout 250 to 2000.

In a preferred but non-limiting embodiment, X is an isocyanate group asshown in the isocyanate terminated PEG prepolymer IIIa, having amolecular weight of ca 1350 and where a₃ ranges from 4 to 5.

Alternatively, X may be an N-hydroxysuccinimide ester as shown in theN-hydroxysuccinimide ester terminated PEG prepolymer IIIb.

Alternatively, the amine reactive moiety having hydrolytically unstableester linkages and electrophilic groups may be prepared from otherhydroxyl terminated polymers such as linear or multi-arm biodegradablepolyesters derived from monomers having hydrolytically unstable esterlinkages, such as caprolactone, lactide, glycolide, dioxanone,trimethylene carbonate or their copolymers, to form isocyanate orN-hydroxy succinimde ester terminated prepolymers. Often it is desirableto have the hydrolysable ester located in the center of the aminereactive moiety with PEG chains surrounding it. In this way, reactionwith a ketimine macromer having a hydrophobic backbone will result in aproduct that hydrolyzes to give water soluble breakdown products.Structures of this type are represented by IVa and IVb below.

Wherein 10<a₄<50, 1<a₄′<2, 2<f₄<6; R₄ is residue of a hydroxy terminatedpolyester synthesized by ring opening polymerization of various lactonesand lactides, e.g. lactide, glycolide, caprolactone, trimethylenecarbonate and p-dioxanone, glycerols and polyalkylene glycol.Alternatively, R₄ may be a polyester synthesized from condensation ofalcohols and acids or esters.

Preferably, isocyanate or N-hydroxy succinimidyl terminated prepolymersIVa or IVb is made by reacting, in a 2:1 molar ratio, a diisocyanato PEGor di-N-hydroxy succinimidyl PEG with a hydroxyl terminated polymer suchas linear or multi-arm biodegradable polyesters. To prepare thesepolyesters, cyclic monomers having hydrolytically unstable esterlinkages, such as caprolactone, lactide, glycolide, dioxanone andtrimethylene carbonate, are heated with an initiator, typically a smallpolyhydroxyl compound, in the presence of a suitable catalyst such asstannous octoate. The initiator's hydroxyloxygen attacks a ring carbonylcreating an ester bond as the ring's original ester linkage is cleavedto open the ring and form a new hydroxyl on the opposite end from thenew ester bond. The new hydroxyl can similarly react with new monomerrings and the chain propagates. Alternatively, a suitable polyester canbe prepared by reacting a polyacid such as adipic acid with an excess ofPEG and a suitable catalyst (e.g. p-toluenesulfonic acid). creating adi-PEG adipate. These polyester syntheses are well known to thoseskilled in the art.

The Moisture Activated Latent Curing Adhesive or Sealant

The amine reactive moiety having hydrolytically unstable ester linkagesand electrophilic groups and the ketimine or aldimine remain relativelystable when mixed together in a liquid mixture in the absence ofmoisture. By comparison, when the two component mixture is subjected tomoisture, the poly(ethylene oxide)imine is “de-blocked” with water toreform the primary amine within about 30 seconds to 3 minutes, whichthen immediately reacts with the electrophilic groups of the aminereactive moiety, as shown in FIG. 1.

In FIG. 1, Z is a functional group formed from the reaction of theelectrophilic group of the amine reactive moiety and the deblocked aminegroup of the ketimine or aldimine, including without limitation, a urealinkage when the electrophilic group is an isocyanate or an amidelinkage when it is an N-hydroxy succinimide ester.

The moisture activated latent curing adhesive formed via the reaction ofpoly (ethylene oxide)imine Ia and isocyanate terminated PEG prepolymerIIIa has been designed to be biocompatible and biodegradable byutilizing predominantly PEG backbones in both Ia and IIIa, andincorporating hydrolytically unstable ester linkages in IIIa that willyield water soluble breakdown products, upon application and use in thehuman body.

As discussed above, a moisture activated latent curing adhesive may alsobe designed to be biocompatible and biodegradable even if the ketimineor aldimine has a hydrophobic backbone, by use of a biocompatible aminereactive moiety having hydrolytically unstable ester linkages located inthe center of the amine reactive moiety with PEG chains surrounding it,for example IVa or IVb, whereby the degradation products of the moistureactivated latent curing adhesive are water soluble.

This type of moisture-activated latent curing adhesive or sealantmixture offers tremendous benefits over the state of the art in terms ofease of use, delivery, handling, tissue adhesion and efficacy. Besidesthe moisture activation ability, key properties exhibited includeeffective sealing, adjustable cure speed, biocompatibility, and storagestability. By judicious selection of the polymer backbones and thelocation of the imine end-groups and the electrophiles, various otherattributes, for example the rate of absorption and the degree ofwater-swellability, etc., may be tailored to suit one's needs.

While the following examples demonstrate certain embodiments of theinvention, they are not to be interpreted as limiting the scope of theinvention, but rather as contributing to a complete description of theinvention.

EXAMPLE 1: Synthesis of Ketimine Ia, Isocyanate Macromer IIIa and TheirGelation

24.42 g of a 4 armed, 4,000 molecular weight amine terminated PEGcompound was weighed into a 250 mL round bottom flask. 31.94 g of methylisopropyl ketone, MIPK (JTBaker) was added followed by the addition of35.8 g of toluene (Aldrich Chemical), 0.30 g of glacial acetic acid (JTBaker) and a magnetic stir bar. The flask was equipped with a Dean Starktrap connected to a reflux condenser and nitrogen inlet for continuousnitrogen blanket and heated with mixing in an oil bath over a magneticstir plate to 125° C. (oil bath temp). The water-toluene azeotrope beganto distill over, separating into separate toluene and water layers inthe Dean Stark trap shortly after the set temperature was reached. Thereaction was allowed to continue in this way for 24 hours followed byremoval of excess toluene, MIPK and acetic acid by distillation. Theproduct was a brown viscous liquid that became a waxy solid uponcooling.

Synthesis of Ketimine Ia

20 g of pentaerythritol ethoxylate (Aldrich chemical company) 100 mL ofacetone (Aldrich chemical company, dried and distilled over calciumsulfate), 20 mL of triethylamine (Aldrich chemical company) wastransferred into a dry round bottomed flask under nitrogen. To this wasadded with stirring, 10.9 g of glutaric anhydride (Aldrich chemicalcompany) using a powder additional funnel. Reaction mixture was refluxedfor 16 hours. Volatiles were evaporated in vaccuo. To residue was added100 mL of water and extracted 1×75 mL of dichloromethane (Aldrichchemical company). The organic extract was dried over anhydrous sodiumsulfate, filtered and volatiles were evaporated first on rotovap andthen under high vacuum at 115° C. for 1 hour to obtain 15.6 g ofmulti-arm acid. 10.0 g of multi-arm acid was transferred into a 250 mLflask and 50 mL of anhydrous dichloromethane was cannulated into theflask while stirring. To the homogeneous mixture was added 6.0 g ofthionyl chloride (Aldrich chemical company) via dry syringe and reactionmixture was refluxed for 1 hour. An FTIR recorded at this stage showedno COOH and presence of COCl. Solvent was evaporated under high vacuumand 30 mL of dry toluene was added to the reaction flask followed byaddition of 6.0 g of azidotrimethylsilane (Aldrich chemical company).Temperature of the reaction mixture was gradually increased andformation of bubbles signified commencement of Curtius rearrangement.After formation of bubbles subsided, reaction flask was held at 80° C.for 10 min to ensure complete conversion of acyl azide to isocyanategroups. Solvent was first evaporated under high vacuum at roomtemperature and then for 5 min at 70° C. to obtain 9.7 g light browncolored liquid.

Synthesis of Isocyanate Macromer IIIa

A mixture comprising ketimine Ia and the tetrafunctional isocyanatemacromer IIIa was allowed to react via the scheme shown in FIG. II.

An Ex-Vivo Arterial Anastomoses Model:

In this model, anastomosis were performed on porcine carotid arteries.This was followed by pressurizing the sutured artery to slowly increasethe fluid pressure inside the sutured artery, until failure was noted bythe leaking of fluid from the suture line. The pressure at failure wasnoted as the baseline and typically ranged between 40-60 mm Hg.

The ketimine Ia, 70% in N-methyl pyrolidone, and the isocyanate macromerIIIa were mixed to form a viscous stable liquid, which was then appliedto the suture line and allowed to cure. The fluid pressure was increasedagain and the pressure at failure was noted. The ketimine based sealantcured after being applied to the wet vessels in 2-3 minutes andpressures at failure ranged from 251 to 537 mm Hg in three separateruns.

EXAMPLE 2: Synthesis of a Triketimine and an Amine Reactive MoietyHaving an Electrophilic Group and Absorbable Ester Linkages

Synthesis of a Triketimine

40 g of amine terminated polypropylene glycol (Huntsman T-403) wasweighed into a 250 mL round bottom flask. 20 g of 4 A° molecular sieveswere added to the flask followed by 24.48 g of methyl isopropyl ketone(JT Baker). The flask was equipped with a magnetic stir bar and heatedto an internal temperature of 70° C. for 3 days. The product wasisolated by centrifugation followed by filtration through a 0.45 micronsyringe filter and was a clear, slightly yellow liquid. Using thetri-amine precursor A allowed for higher crosslink density materials andhigher strength. The reaction is as depicted above.

An amine reactive moiety having electrophilic groups and absorbableester linkages was prepared according to FIG. III. Specifically, 5.32 gof an isocyanate terminated 2000 molecular weight PEG powder wasweighed, in a glove box under dry nitrogen, into a 50 mL round bottomflask. 0.41 g of a dried 600 molecular weight liquidcaprolactone/glycolide diol was added followed by addition of 2.36 g ofdry N-methyl pyrolidone. The reaction mixture was heated in an oil bathover a magnetic stir plate, under dry nitrogen, to 65° C. at which pointa single clear phase resulted. 0.08 g of a 1% solution of Bicat H(Shephard chemical) bismuth catalyst in toluene was added. The reactionmixture was heated to 80° C. and kept at that temperature for 4.5 hours.The product was a clear slightly brown liquid that became a waxy solidupon cooling. The wt % free isocyanate as determined by titration was1.65%

Biocompatibility of the Two-Component Cured System

The triketimine was mixed with the degradable PEG/polyester diisocyanatein a 1:1 equivalent ratio of NCO: Ketimine prior to application to atissue and then implanted in rats for a subcutaneous tissue reaction andabsorption study.

An exploratory 7, 14, 28-day subcutaneous tissue reaction and absorptionstudy of the above system in rats was carried out. At days 7, 14 and 28post implantation, the tissue reaction to the saline control wascharacterized by minimal sub-acute inflammation, minimal to mildcapillary proliferation and minimal fibrosis. At day 7, the sealantresulted in mild to moderate chronic inflammation, minimal to mildcapillary proliferation and the presence of a generally mild amount ofthe free sealant material. At day 14, the sealant material hadphagocytized by the histiocytes and was interpreted to be absorbed in40% of the implant sites. At day 28, the sealant material wasinterpreted to be absorbed at all the implant sites. At days 14 and 28,a decrease in severity of the inflammatory reaction was observed. At day28, mild to moderate histiocytosis was observed in the inguinal_lymphnode of all the animals. These histiocytes were interpreted to havephagocytized the sealant material. No systemic effects were observed inthe kidneys, liver and spleen, there appears to be a low or no incidencefor acute systemic toxicity. The above was considered a favorableresponse of the animal to the sealant formulation.

What is claimed is:
 1. A biocompatible moisture activated latent curingadhesive or sealant mixture comprising (a) a ketimine or aldiminerepresented by formula I:

where 3000≧a₁≧3; 6≧f ≧2; R₁ is a residue of a polyol; R₁′ and R₁″ areeach an alkyl group, alkoxy group, acetoacetate or a hydrogen; and atleast one of R₁′ or R₁″ is an alkyl group having from about 1 to 20carbon atoms; and (b) an amine reactive moiety represented by formulaIVa:

wherein 10<a4<50; 1<a4′<2; 2<f4<6; R₄ is residue of a biodegradablehydroxy terminated polyester selected from the group synthesized by ringopening polymerization of a lactide, glycolide, caprolactone,trimethylene carbonate or dioxanone with a glycerol or polyalkyleneglycol initiators.
 2. The moisture activated latent curing adhesive orsealant mixture of claim 1, wherein the ketimine is represented byformula Ia

where a₁ ranges from about 18 to
 22. 3. The moisture activated latentcuring adhesive or sealant mixture of claim 1, where R₁ is a residue ofpentaerythritol, glycerol or polyalkylene glycol; and R₁′ and R₁″ areeach a methyl, ethyl, isopropyl, isobutyl, ethoxy, carbalkoxy,acetoacetate or a hydrogen.
 4. The moisture activated latent curingadhesive or sealant mixture of claim 3, where a₁ ranges from about 3 to500; f ranges from 2 to 4; R₁ is a residue of pentaerythritol; and R₁′and R₁″ are each a methyl and isopropyl group.
 5. The moisture activatedlatent curing adhesive or sealant mixture of claim 4, where a₁ rangesfrom about 18 to 22, and f is 4.